Take it all with a big grain of salt, as neither Twitter nor the Mexican government has verified the authenticity of several messages.
Guzman's escape through a tunnel below a maximum-security prison Saturday was an instant sensation on social media, where the drug lord was already a folk antihero.
Attention also almost immediately zoomed toward a Twitter account bearing the name of Guzman's son, Ivan, who has been accused of helping run Guzman's Sinaloa drug cartel.
The account, @lvanArchivaIdo -- the lowercase "L" near the end is actually a capital "I" -- sent two portentous-seeming tweets in the days and weeks before the escape.
In a May 8 tweet, the account said that "the general will soon return."
Then, in a July 6 tweet, the account said, "Everything comes for those who know how to wait."
The Trump threat comes from an account that @lvanArchivaIdo says belongs to El Chapo: @ElChap0Guzman. (The "O" is actually the number "0.")
The account, which claims to be the "official" Guzman account, has been used to send tweets the whole time El Chapo has been in prison.
After the Saturday prison break, the account, using the first person, wrote that El Chapo had reunited with two of his sons.
The account also tweeted a crude and unprintable threat at Trump, the Republican presidential candidate who has been criticizing Mexican immigrants in the U.S. illegally.
These tweets have made lots of waves on social media and in the news media, but it's unclear whether they are authentic.
"I am told they are apocryphal," Mexican Deputy Interior Minister Roberto Campa told Reuters.
A Twitter spokesman told the Los Angeles Times that it was company policy not to comment on individual accounts, but he noted that neither account carried the company's blue check marks indicating authentic ownership.
The accounts did not immediately respond to messages seeking comment.
It's worth noting that both seem to use similar capitalization and punctuation -- and tend to tweet similarly vague aphorisms rather than specific information.
There are a few general ways to determine whether social media accounts are authentic. One of the best is to contact the alleged owners directly, in person or through a different, verified channel. In the case of wanted drug lords, this is a little difficult.
Another clue is whether the accounts post exclusive photos or information that could be possessed only by the real owners. Do the alleged Ivan tweets really predict El Chapo's escape? Or are they vague bluster that seems portentous only after the fact?
A third form of verification is through officials -- government investigators who have perhaps been able to obtain forensic information about where a post originated, or are able to corroborate details from published photos with other information gathered about a suspect.
A FBI spokeswoman in Washington referred The Times to the bureau's New York field office, which did not immediately respond to a message seeking comment.
The tweets from @lvanArchivaIdo also come from a different Ivan Guzman Twitter account than the one that made news last year -- @_IvanGuzman_ -- for tweeting photos of fancy cars, gold-plated AK-47s and big piles of cash.
That account, @_IvanGuzman_, hasn't tweeted since January.
It is highly doubtful that Guzman's son posted pictures of his father online or threatened Trump on Twitter, Mike Vigil, former chief of international operations for the Drug Enforcement Administration, said in an interview Tuesday.
Posting the pictures, which appeared on the Spanish-language "El Blog Del Narco," would have given away his father's location, and threatening Trump would have required Guzman's son to know or care who Trump is, Vigil said.
"When a big event happens, you get a lot of pranksters that come out and put stuff like that out," Vigil said.
Times staff writer Christina Littlefield contributed to this report.